Midwest
Commutative
Algebra
Conference
at
PURDUE
Purdue University
West Lafayette, Indiana
August 3  7, 2015
Poster Session
During the conference, on August 5 from 2:50 to 5:00 pm, there will be a poster session, which will be
held in the atrium in front of the lecture room (Lawson 1142).
The poster session is particularly targeted to peridoctoral students
who are given the opportunity to advertise their research among
the conference participants in a very informal, relaxed but conducive
atmosphere. It is our hope that junior researchers will benefit from
this experience by obtaining feedback and suggestions for future lines
of investigation from more experienced researchers.
Directions/Suggestions:
We will provide large poster displays where you can show your poster.
It would be wiser though if you bring your
'favorite' scissor, push pins, glue, tape, markers from home as we
cannot guarantee that we can provide you with all the supplies that
you might want/need.
We also encourage you to read the material posted at the following links on how
to plan and prepare a poster presentation:

http://www.ce.umn.edu/~smith/supplements/poster/guide.htm

http://www.siam.org/meetings/guidelines/poster.php

http://www.siam.org/meetings/guidelines/presenters.php
Poster Titles/Presenters

Tensor product surfaces and linear syzygies
Eliana M. Duarte, University of Illinois at UrbanaChampaign
Abstract:
A tensor product surface is the image of a map φ : P^{1} × P^{1} → P^{3}.
Such surfaces arise in geometric modeling, and it is often useful to find the implicit equation for the surface.
In this poster we explain how the implicit equation can be obtained from the syzygies of the defining
polynomials of the map via an approximation complex. In particular the existence of a linear syzygy
allows for a straightforward description of the implicit equation of the image from which we can describe
part of the codimension 1 singular locus. This is joint work with Hal Schenck.

ZeroDivisorsCupLength of OrlikSolomon Algebras
Nathan Fieldsteel, University of Illinois at UrbanaChampaign
Abstract:
For an algebra over a field, the zerodivisorscuplength is an integer invariant which generalizes the
ordinary cup length and contains information about the obstructions to finding continuous motion
planning algorithms for spaces with cohomology ring isomorphic to that algebra. We are interested in
computing the zerodivisorscuplength for OrlikSolomon algebras, which are the cohomology rings of complements of complex hyperplane arrangements.

GTheory of hypersurface singularities
Zachary Flores, Colorado State University
Abstract:
We discuss the recent advancements in computing lower Ggroups for the category of finitely generated modules over
hypersurface singularities of finite type. We also discuss computations and further directions in the structure of the Gtheory of these rings.

Blowing up finitely supported complete ideals in a regular local ring
Youngsu Kim, University of California at Riverside
Abstract:
We investigate the singularities of the blowup of a finitely supported ideal in a regular local ring.
We show that if the normalized blowup of a finitely supported ideal is factorial, then it is nonsingular.
This is a generalization of the theorem of Lipman and HunekeSally.
This is a joint work with William Heinzer and Matthew Toeniskoetter.

On minimal free resolutions of the associated graded rings of Gorenstein monomial curves
Pinar Mete, Balikesir University
Abstract:
Our main goal is to give the minimal free resolution of the associated graded ring gr_{m}(A),
where A = k[[x_{1}, . . . , x_{n}]]/I(C), of Gorenstein monomial curve C
in embedding dimension four under some restrictions on the generators in the
defining ideal I(C) and also to study to characterize the Hilbert function of the
local ring A.

Rees algebra and almost linearly presented ideals
Vivek Mukundan, Purdue University
Abstract:
We present the defining ideal of Rees algebra of grade 2 perfect ideals whose presentation matrix is almost linear.
We also introduce the notion of iterated Jacobian duals along with its application in the case of ideals whose second analytic deviation is one. Joint work with Jacob A Boswell.

When does the Frobenius splitting number function have a second coefficient?
Thomas Polstra, University of Missouri
Abstract:
Suppose that (R,m,k) is a local normal Ffinite domain of prime characteristic p > 0, with perfect residue field
k, dimension d, and suppose that I is an mprimary ideal.
It has been shown by Huneke, McDermott, and Monsky that there is a coefficient b ∈ R such that for
λ(R/I^{[q]})=e_{HK}(I)q^{d}+bq^{d1}+O(q^{d2})
where q=p^{e} is a power of the characteristic and e_{HK}(I)
is the HilbertKunz multiplicity of I. Given such a ring it is now natural to ask when does the Frobenius splitting number
function have a second coefficient, i.e., when does there exist a t ∈ R such that a_{q} =
sq^{d}+tq^{d1}+O(q^{d2}) where a_{q} is the Frobenius
splitting number function of R and s is the Fsignature of R.
We develop some conditions which imply the existence of a second coefficient of the Frobenius splitting number function
and ask whether these conditions can be met outside cases where Huneke, McDermott, and Monsky's results already
imply that the Frobenius splitting number function has a second coefficient.

Closure operations that induce Big CM modules and algebras
Rebecca R.G., University of Michigan
Abstract:
We review axioms for Dietz closures, which imply the existence of big CM modules, and give an additional axiom sufficient for big CM algebras.
We show under mild conditions on R that all Dietz closures are trivial if and only if R is regular.

Deviations of graded algebras
Alessio Sammartano, Purdue University
Abstract:
The deviations of a graded algebra are a sequence of numbers that determine its Poincaré
series and arise as the number of generators of certain DG algebra resolutions. While these invariants
encode important homological information, they are considerably hard to determine explicitly even in
simple examples. We study extremal deviations among those of algebras with a fixed Hilbert series and
the asymptotic growth of deviations for Golod rings and for algebras presented by certain edge ideals.
This is joint work with Adam Boocher, Alessio D'Alì, Eloísa Grifo, and Jonathan Montaño.

Pullback diagrams and Kronecker function rings
Simplice TchamnaKouna, Georgia College
Abstract:
We present the notion of Kronecker function subring of a ring extension R ⊆ S. For each ring extension
R ⊆ S and a star operation * on R ⊆ S, we study the properties of the
Kronecker subring Kr(R,*, S) of S(X) defined by Knebusch and Kaiser. We also study the
behavior of the ring Kr(R,*, S) in pullback diagrams.

On the top local cohomology modules
Tugba Yildirim, Istanbul Technical University
Abstract:
Throughout, let R denote a commutative Noetherian ring, I an ideal of R and M an Rmodule.
Let cd(I,M) denote the cohomological dimension of M with respect to I.
In a joint work with Vahap Erdoǧdu, for an Rmodule M with cd(I,M)=c,
we show the existence of a descending chain of ideals I = I_{c} ⊋ I_{c1}
⊋ … ⊋ I_{0} of R such that for each 0 ≤ i ≤ c1,
cd(I_{i},M)=i and that the top local cohomology module H^{i}_{Ii}(M)
is not Artinian. We then give sufficient conditions for an arbitrary integer t to be a lower bound for cd(I,M),
and use this to conclude that in noncatenary Noetherian local integral domains, there exist prime ideals that are not
set theoretic complete intersection. For an Rmodule M of dimension n such that H^{n}_{m}(M)
≠ 0 (where R is local with unique maximal ideal m), we also resolve the Artinianness and nonArtinianness
of top local cohomology modules, H_{I}^{cd(I,M)}(M), in all cases except in the case
cd(I,M) = n1 and dim(R/I+Ann(M)) >1 for which we have some sorter results under certain conditions.